agreement between this empirical equation and the model tests is shown in 

 Figure 2. Equation [3] therefore provides a baseline for predicting the 

 elastic or inelastic collapse of a near-perfect, initially stress-free, 

 deep spherical shell with ideal boimdaries. 



Tests were also conducted at the Model Basin to determine the 



relationship between unsupported arc length and the elastic and inelastic 



5 

 collc5)se strength of machined shallow spherical caps with clamped edges. 



Although previous data in the literature showed wide disagreement in ex- 

 perimental results, these tests followed a very definite pattern. The 

 test results for the inelastic case, which is of particular interest, are 

 plotted in Figure 3. The ordinate is the ratio of the experimental collapse 

 pressure to the eii5)irical pressure, and the abscissa is the nondimensional 



parameter 9 defined as 



0.91 L 



for u = 0.3 [5] 



/Rh 



where L is the unsupported arc length of the shell. The results are 

 plotted in families of curves which basically represent varying degrees of 

 stability; shells with the lowest values of Pg/P-i are the most stable. The 

 results demonstrate that for 9 values greater than approximately 2.2, the 

 effect of claiiping the edges diminishes as the shells become more stable. 

 Although all of the test results discussed thus far have been for 

 near-perfect models, they do provide the basis for the analysis of spherical 

 shells with initial imperfections. Equations [3] and [4] adequately predict 

 the collapse of near-perfect models. Figure 3 indicates that the collapse 

 of a spherical shell with a 9 value greater than about 2.2 is relatively in- 

 dependent of the boundary conditions. Thus the collapse strength of shells 

 with initial Imperfections depends primarily on the local geometry over a 



critical arc length. These two observations form the basis of the im- 

 perfection analysis developed in Reference 6. In this analysis the general 

 form of Equations []ljand [Ujbecomes 



h 



p-^ = 1.21 E(-^] [6] 



